Fatigue Crack Propagation in Pressurized metallic Fuselages

Stiffened panels are widely used in aircraft wing and ftiselage structures. As a result of the cyclic nature of the loads associated with each flight, and material and manufacturing defects it is known that wide spread fatigue cracks may develop particularly around high stress regions such as fastener holes. This simultaneous development of relatively small fatigue cracks at multiple sites in the same structural element can give rise to their joining to form one large crack. This main crack, resulting from the multiple site damage (MSD) may cause immediate and complete failure of the structure.The effect of multiple site damage on the fracture strength of a stiffened sheet is examined using the Strip Yield Model of a crack. This model is relatively simple to apply and has contributed significantly to the fracture analysis of unstiffened structures and, to a more limited extent, to the analysis of stiffened structures. Following previous developments the MSD is represented by a discontinuous strip yield zone ahead of the main crack. The solution is extended in the present work to a crack in a stiffened sheet and results are determined for the crack tip opening displacement and the strip yield zone length for a crack in a typical MSD distribution. The model is used to compare the effect of MSD on the main crack for these structural variables. INTRODUCTION The Displacement Compatibility Method (DCM), has been used extensively (see citations in ref 1) for the analysis of cracked, reinforced sheets typical of those used in the aircraft industry. Applications of the DCM have proved both efficient and versatile for the determination of attachment forces and stress intensity factors in stiffened sheet structures. For high strength materials it is possible to use the principles of Linear Elastic Fracture Mechanics (LEFM) and to base the analysis on the Stress Intensity Factor of the crack. For medium and low strength materials where yielding at the crack tip may exceed the limits required for LEFM to apply it is necessary to use the principles of Non-linear Fracture Mechanics (NLFM). One method of doing this is to use a Strip Yield Zone (SYZ) model of the crack for which the fracture analysis is based on the Crack Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 566 Localized Damage Tip Opening Displacement (CTOD) or Energy Release Rate of the crack. The SYZ model [2] has been used in the analysis of reinforced sheets structures [35]. This previous work was restricted the a single lead crack in the stiffened sheet. The model has also been extended to the analysis of multiple cracks [6] in which the interaction between the multiple cracks, such as occurs in MSD, was accounted for by using the displacement and stress field for the single crack together with the crack line Greens Function for a single crack in a Schwarz alternating process. In the present work the MSD is represented by introducing regions of zero traction into the strip yield zone between which are regions of uniform traction having a magnitude equal to the yield strength of the material. This representation of the MSD enables the single SYZ model to be directly entended to take account of the effect of multiple site damage by having the strip yield zone distributed discontinuously. Each gap in the yield zone tractions corresponds to the region of damage and each junction corresponds to the yielded ligament between the damage sites. A similar approach, based on a dislocation model of the MSD, has been used [7]. This model was used to analyze the effect of MSD on a lead crack in an unstiffened sheet and then create a modified single SYZ model for the analysis of stiffened sheets. In the present work the MSD is represented as a discontinuous distribution of tractions for both the unstiffened and stiffened sheet. THEORETICAL FORMULATION AND SOLUTION OF EQUATIONS The analysis is based on the complex variable technique due to Muskhelishvili [8] which states that the stress/displacement state within a multiply connected, two dimensional body subjected to in-plane loading may be completely specified in terms of two complex stress functions which can be written in series form. The system equations are formed by satisfying equilibrium of forces at, and compatibility of displacements between the attachment points, and by satisfying the strip yield crack condition that the stresses be bounded at the tip of the yield zone (Dugdale Condition). The system equations are solved for the unknown distribution of attachment forces and the unknown ratio of the sheet stress to the yield stress of the sheet material.The CTOD of the crack is determined from the attachment forces and the applied stress ratio for a specified distribution of MSD in the yield zone. CONFIGURATION STUDIED The configuration to be studied in the present work is shown in Fig. 1. It consists of an infinite sheet containing a lead crack of length 2a centered at the origin of the coordinates (x = 0,jy = 0). The lead crack has a series of of collinear cracks symmetrically located on either side of each tip which are joined by ligaments at the yield stress of the material the outer ones of which have strip yield zones at their tip. The region of MSD and the outer tip yield zones extend a distance s from the tip of the lead crack. The collinear cracks, which represent the MSD, are located under doubly riveted stiffeners with a stiffener across the Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 Localized Damage 567 centre of the lead crack. The sheet is subjected to a uniform stress a perpendicular to the crack line. Fig. 1 Lead crack and Multiple Site Damage in a Uniformly Stressed Stiffened Sheet In general the sheet is reinforced by arbitrarily spaced stiffeners parallel to the yaxis. The stiffeners are attached to the sheet at discrete points symmetrically either side of the x-axis. The first attachment point is PQ from the x axis and all the other attachment points are a distance p apart . The attachment points are assumed to be represented by localised forces at the center of a rigid insert of diameter d. The sheet has a modulus of elasticity E, Poisson's ratio v and thickness t. The Young's modulus and area of each stiffener is E$ and Aj respectively. The effect of the in-plane and out of plane bending stiffness of each stiffener is assumed negligible compared to its axial stiffness, In the present work only a symmetrical distribution of two equal length MSD cracks, each side of the lead crack, is considered although the formulation allows for an arbitrary length and position of the MSD cracks It is also assumed that the center of the MSD cracks are symmetrically located across the center line of the attachments, Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 568 Localized Damage The parameters used for modelling the stiffened sheet are given in Table 1 and represent a typical aircraft stiffened structure [3]. The stiffeners were attached at 15 points either side of the crackline along each rivet line. Parameter Sheet Modulus E Sheet Yield Strength <jy Stiff ener Modulus E,. Sheet Poissions Ratio u First Rivet Pitch p. Rivet Pitch p Sheet Thickness t Stiffener Area A Rivet Diameter d Attachment Line Spacing h Stiffener pitch b Lead Crack Length a MSD Crack Size d, and d, Magnitude 73.8 GVm ' 386 MVm 74.5 GNm* 0.3 38.1 mm 38.1 mm 18.1 mm 1710mm' 8 mm 58.4mm 185.4mm 148.2 mm 10 mm Table 1. Dimensions and Material properties for the stiffened sheet containing MSD COMPARISION WITH KNOWN SOLUTIONS Table 2 shows the crack tip opening displacement for the SYZ model normalised with that for a SYZ crack in an unstiffened sheet. The SYZ crack is modeled as a single crack (^ = = 0) and by simulating this single crack by modelling the SYZ with a longer strip yield zone and eliminating part of the zone with contiguous MSD regions to give the same strip yield length as the single crack model. It can be seen that these two models give identical results as is to be expected. a a + s 0.1 0.5 0.9 Unstiffened Sheet

Delamination propagation in fibrous laminates is often accompanied by development of a damage zone, within which intact fibers bridge the crack faces that constitutes a major toughening mechanism. A direct experimental assessment of the crack closure tractions due to bridging fibers is a challenging task. In addition, when the length of the bridging zone becomes comparable with the laminate linear dimensions, referred to as large scale bridging, the extent of bridging can be influenced by the laminate size and layup. Hence, traction-separation relations used in computational methods to predict fracture do not always rely on solid experimental evidence of large scale bridging and for numerical convenience simple linear traction-€“separation expressions are often considered. In this work, a semi-experimental methodology is employed to identify the contribution of large scale bridging to delamination resistance of unidirectional and cross-ply carbon fiber/epoxy laminates. Double cantilever beam specimens of different thickness are prepared and subjected to monotonic and fatigue mode I loadings. In selected specimens, optical fibers with multiplexed fiber Bragg grating (FBG) sensors are embedded. The strain distribution in the vicinity of the crack plane is monitored by FBG sensors. The strain data are used in an inverse identification procedure to quantify the bridging tractions and the energy release rate (ERR) due to the bridging. Subsequently, the identified tractions are implemented in a cohesive zone model to simulate delamination propagation. Employing the aforementioned approach, specimen thickness dependence of large scale bridging in delamination of unidirectional laminates is investigated. The results indicate that onset of delamination is independent of the specimen geometry. However, the extent of the bridging zone and the plateau level of delamination resistance both significantly increase with increasing the specimen thickness. The maximum traction at the crack tip is independent of the specimen size while the length of the steady state bridging zone scales linearly with the thickness of laminate. Moreover, the nonlinear rate of tractions decay is inversely proportional to the specimen thickness. It is shown that the tractions decay parameter is controlled by the curvature of the specimen arm. Evaluation of bridging effects on fatigue delamination of unidirectional laminates indicates that the stable phase of fatigue crack growth is more extended in the thicker specimens and the critical ERR increases by increasing the specimen thickness. Similar to the trend observed in monotonic delamination, fatigue delamination in the thicker specimens is accompanied by a longer bridging zone in which the bridging tractions decay with a lower rate. The maximum bridging traction at the crack tip is independent of the specimen thickness. It is demonstrated that the traction-separation relation and the ERR due to the large scale bridging depend on the ply orientations at the crack interface whereas ERR values at the onset of delamination are almost the same. As compared to delamination of a unidirectional specimen, crack propagation in cross-ply laminate is accompanied by a smaller bridging zone, but fiber bridging in the cross-ply specimens is more efficient. The adopted methodology in this work provides a robust assessment of large scale bridging and is a step towards a better understanding of delamination in fiber reinforced composites.

Stiffened panels dominate aircraft structure with their design potential for high strength with low weight. This characteristic is due to the use of high strength materials and the stable post-buckling response of stiffened panels to compression and shear loading. By permitting the skin between stiffeners to buckle in service at defined percentages of the panel ultimate load, panel strength-to-weight ratio is maximised. Advances in strength and damage tolerant characteristics of available aerospace materials offers opportunities for increased working and limit stresses. To fully exploit material improvements as weight savings on aircraft primary structures, it is desirable to enhance the buckling stability of stiffened panels. To further increase structural efficiency of integrally machined stiffened panels it is plausible to vary the skin thickness between stiffeners to increase the skin stability without increasing material volume, [1]. Additionally, considering the issues surrounding the damage tolerance of integrally stiffened panels, local skin profiling may be designed to retard fatigue crack growth, improving the damage tolerance characteristics of the structure, [2] and [3]. As static strength performance gains are achieved by changing the initial form and magnitude of skin buckling, experimental capture of skin deformation behaviour under test is required to validate local profiling analysis and optimisation tools. The work presented in this paper documents the experimental programme undertaken to validate strength analysis tools by capturing initial skin buckling behaviour and post-buckle mode-jumping of integrally machined stiffened panels with local skin profiling.

The 22 wt.% Cr, fully ferritic stainless steel Crofer®22 H has higher thermomechanical fatigue (TMF)- lifetime compared to advanced ferritic-martensitic P91, which is assumed to be caused by different damage tolerance, leading to differences in crack propagation and failure mechanisms. To analyze this, instrumented cyclic indentation tests (CITs) were used because the material’s cyclic hardening potential—which strongly correlates with damage tolerance, can be determined by analyzing the deformation behavior in CITs. In the presented work, CITs were performed for both materials at specimens loaded for different numbers of TMF-cycles. These investigations show higher damage tolerance for Crofer®22 H and demonstrate changes in damage tolerance during TMF-loading for both materials, which correlates with the cyclic deformation behavior observed in TMF-tests. Furthermore, the results obtained at Crofer®22 H indicate an increase of damage tolerance in the second half of TMF-lifetime, which cannot be observed for P91. Moreover, CITs were performed at Crofer®22 H in the vicinity of a fatigue crack, enabling to locally analyze the damage tolerance. These CITs show differences between crack edges and the crack tip. Conclusively, the presented results demonstrate that CITs can be utilized to analyze TMF-induced changes in damage tolerance.

Fracture analysis of reinforced concrete deep beam strengthened with carbon fiber-reinforced polymer (CFRP) plates was carried out. The present research aimed to discover whether crack propagation in a strengthened deep beam follows linear elastic fracture mechanics (LEFM) theory or nonlinear fracture mechanics theory. To do so, a new energy release rate based on nonlinear fracture mechanics theory was formulated on the finite element method and the discrete cohesive zone model (DCZM) was developed in deep beams. To validate and compare with numerical models, three deep beams with rectangular cross-sections were tested. The code results based on nonlinear fracture mechanics models were compared with the experimental results and the ABAQUS results carried out based on LEFM. The predicted values of initial stiffness, yielding point and failure load, energy absorption, and compressive strain in the concrete obtained by the proposed model were very close to the experimental results. However, the ABAQUS software results displayed greater differences from the experimental results. For instance, the predicted failure load for the shear-strengthened deep beam using the proposed model only had a 6.3% difference from the experimental result. However, the predicted failure load using ABAQUS software based on LEFM indicated greater differences (25.1%) compared to the experimental result.

Coupling an XFEM code for linear elastic fracture propagation to a viscous flow model. GeoComputation 2019

Fretting fatigue crack propagation under out-of-phase loading conditions using extended maximum tangential stress criterion

Anisotropic materials gain importance in industry pushed forward by new applications, from wood construction, single crystals for photovoltaic applications or aerospace turbines, to Additive Manufactured materials. But due to the lack of certified damage tolerance models to guarantee their resistance to failure, their use in aerospace or nuclear sensitive components whose failure must be avoided at all costs is limited. In this context, we present herein a new experimental benchmark, instrumented by Digital Image Correlation, aiming to test quasistatic crack propagation models for anisotropic linear elastic materials, for instance phase field variational approaches. The benchmark is based on Compact Tensile and Compact Tensile Shear samples printed by Fused Deposit Modeling of polycarbonate threads. The flexibility of the printing process is used to produce specimens that exhibit directional dependence of the fracture toughness. Fracture experiments with these samples have been designed to enter in the framework of two-dimensional (2D) Linear Elasticity Fracture Mechanics (LEFM) with strong fracture anisotropy, while avoiding additional complexities by preserving isotropic elasticity and quasistatic propagation. Close comparisons with the experiments demonstrate that the generalized maximum energy release rate criterion accurately predicts crack propagation. While serving as a benchmark, these experiments also lay the foundation for a better fundamental understanding of crack propagation in anisotropic materials, beyond FDM printed parts.

Study on fatigue damage tolerance of rail steel materials using peridynamics

The excellent durability performance of Glare, a thin fiber metal laminate (FML) material system, is now being proven in service. This has motivated work towards the application of FMLs to thicker structures driven by damage tolerance. In order to fully characterize the crack growth life of such materials, models are necessary that can account for the unique aspects of material systems under consideration, including non-uniformity of composition and stress states, and the resulting complex damage state involved in fatigue crack growth. This thesis presents a generalized analytical model for the prediction of fatigue crack and delamination growth in FMLs of arbitrary lay-up, including differing metal alloys, different thickness layers, and different combinations of reinforcing composite layers. Cracks in each layer, and delaminations in each interface, are allowed to grow separately, with the interactions of the damage throughout the laminate taken into account. The model is structured in a modular and iterative fashion. Modules for determining the load redistribution around damage and the strain energy release rate of delamination have been derived and independently validated through comparison to finite element analyses. A series of tests with thick fiber metal laminates of varied construction was carried out to verify the overall crack growth predictions of the model. While some discrepancies between the results and predictions for the most complex laminates suggest that refinement of the delamination strain energy release rate formulation is needed, many of the test results were accurately predicted, demonstrating the suitability of this model for use in design and analysis of thick FML structures.

The objective of this study was to follow the crack propagation in the tooth foot of a spur gear by using Linear Elastic Fracture Mechanics (LEFM) and the Finite Element Method (FEM). The tooth foot crack propagation is a function of Stress Intensity Factors (SIF) that play a very crucial role in the life span of the gear. A two-dimensional quasi-static analysis is carried out using a program that determines the gear geometry, coupled with the Finite Element Code (ANSYS). The study estimates the stress intensity factors and monitors their variations on the tooth foot according to crack depth, crack propagation angle, and the crack position. An appropriate methodology for predicting the crack propagation path is applied by considering gear tooth behavior in bending fatigue. The results are used to predict/prevent catastrophic rim fracture failure modes from occurring in critical components.

The researches on the behavior of very-high-cycle fatigue (VHCF) for high strength steels have become a new branch in the field of metal fatigue since 1980s. The characteristics of crack initiation and propagation for high strength steels in VHCF regime differ from those in low cycle and high cycle fatigue regimes. One of the most distinct phenomena for VHCF regime is the interior or subsurface crack initiation at inclusions or at other inhomogeneities. In fact, the period of crack initiation and early growth dominates the fatigue life, which is extremely evident for the fatigue process containing VHCF regime. This paper attempts to further investigate the crack initiation with the morphology of so-called fish-eye and fine granular area (FGA) or optical dark area (ODA) for high strength steels. Fatigue tests were carried out on a high carbon low alloy steel by using rotating bending (52.5Hz) and ultrasonic push-pull (20kHz) machines and the fatigue fracture surfaces were examined by scanning electron microscopy. The present results together with the previous ones showed the data of the stress intensity factor range (SIF) as a function of the dimension for fish-eye and FGA. The results also showed the data of FGA dimension as a function of related inclusion size. Based on the present results and the ones from literature, two models of fatigue life estimation were developed. One was taking into account the size of plastic zone at crack tip in relation with the value of SIF at FGA. The other was considering the fatigue damage cumulative process in relation with the microscopic parameters (inclusion size and FGA size) at the fracture region along with macroscopic quantities (tensile strength and stress level). The estimations are in good agreement with experimental results.

A 2D numerical modelling of plasticity induced crack closure on MT specimens

Influence of composition on mechanical behaviour of porcelain tile. Part II: Mechanical properties and microscopic residual stress

Geological Carbon Sequestration (GCS) is one of the ways to store a large quantity of CO2 in a subsurface to combat climate change. The main aim of the thesis is to expand the scope of the element-free Galerkin (EFG) method in its application to multiphase flow for CO2 injection and storage in deep saline aquifers and multiscale modelling of fracture in wet porous media within the linear elastic fracture mechanics domain. Specific objectives include an accurate assessment of stress intensity factors for varying crack lengths and the study of crack propagation in a representative reservoir rock and caprock materials.